Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#3567 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,20)(19,24)(21,26)(28,29)(30,33)(31,36)(32,37)(34,38)(35,40)(39,41)(42,43);(13,17)(18,23)(19,24)(25,27)(29,30)(31,38)(35,37)(39,43);(12,13)(14,18)(15,19)(16,17)(20,23)(21,25)(22,24)(26,27)(28,30,33,29)(31,36,38,34)(32,37,40,35)(39,42,43,41);(12,14,16,20)(13,18,17,23)(15,21,22,26)(19,25,24,27)(28,31)(29,34)(30,36)(32,39)(33,38)(35,41)(37,42)(40,43);(12,15,16,22)(13,19,17,24)(14,21,20,26)(18,25,23,27)(28,32)(29,35)(30,37)(31,39)(33,40)(34,41)(36,42)(38,43)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2299);